Lattice-cavity solitons in a degenerate optical parametric oscillator

We predict the existence of lattice-cavity solitons for a quadratic nonlinear cavity, where the linear losses are compensated for by the optical pump at second harmonic (degenerate optical parametric oscillator), and which is endowed with a one-dimensional photonic lattice. In the limit of strong discreteness (weak coupling) this kind of soliton solution contains as the subclass the quadratic discrete cavity solitons. The nonlinear coupling between the Bloch waves of different photonics bands allows for the formation of a reach variety of localized solutions. In particular, different types of multiband lattice-cavity solitons can be identified. Most types of lattice-cavity solitons do not have counterparts, neither in conventional planar microresonators nor in genuine discrete systems as an array of weakly coupled cavities. We show that these solitons may destabilize as a consequence of the competition between Bloch waves of different photonic bands.